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Short and long bonds in liquid tellurium
Journal of Non-Crystalline Solids 250±252 (1999) 447±452
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Short and long bonds in liquid tellurium Y. Kawakita a
a,* ,
M. Yao b, H. Endo
c
Faculty of Science, Department of Physics, Kyushu University, 4-2-1 Ropponmatsu, Fukuoka 810-8560, Japan b Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan c Faculty of Engineering, Fukui Institute of Technology, 3-6-1 Gakuen, Fukui 910-8505, Japan
Abstract Liquid tellurium (Te) is metallic, which is caused by the strong interaction between neighbouring chain-molecules. With decreasing temperature from the melting point (450°C) to a supercooled state (250°C), liquid Te undergoes a transition from a metal to a semiconductor (M±S transition) being accompanied by volume expansion. Our EXAFS data for supercooled liquid Te were carefully analyzed by adopting a `model-independent' method. It is found that the and long(2.95 A) covalent bonds and short chains in liquid Te with metallic nature are composed of short(2.80 A) that the long bonds vanish on the M±S transition. The M±S transition described above also occurs by the addition of an alkali to liquid Te. The relation of the existence of long covalent bond and the metallic behavior is explained in term of charge ¯uctuations in the chain molecule. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Various measurements such as EXAFS, neutron scattering and conductivity have been carried out on liquid Te by our group [1,2]. Important ®ndings are that liquid metallic Te near the melting point has a covalently bonded chain structure composed of short and long bonds [1]. The existence of two-type bonds leads to the key question: What is the mechanism that links the metallic properties with the bonding con®guration? Recent results for the deeply supercooled liquid Te and the liquid alkali±Te mixtures provide essential information [1,2]. When liquid Te is supercooled to 250°C, it undergoes a transition from a metal to a semiconductor (M±S transition) being accompanied by a volume expansion [3]. We sug-
* Corresponding author. Tel.: +81 92 726 4734; fax: +81 92 726 4728; e-mail: [email protected]
gested based on analysis of EXAFS data that the fraction of long bonds decreases on approaching to the M±S transition region [1]. The M±S transition is also observed when alkalis such as Na, K, Rb and Cs are added to liquid Te. These eects are accompanied by a decrease of interchain correlation [2,4] and a decrease of the long bond fraction [2]. The large electronegativity dierence suggests the substantial charge transfer from the alkali atom to the Te. In fact, the compositional and temperature dependence of conductivity are almost independent of the alkali species [2]. This M±S transition observed for the liquid alkali±Te mixtures also leads to the assumption that the presence of long bonds is closely related to the metallic properties of liquid Te. The purpose of this paper is to establish a microscopic scenario for the M±S transition in terms of the fraction of long bonds on a basis common to both supercooled liquid Te and liquid alkali±Te mixtures. To recon®rm the presence of
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 2 7 5 - 6
448
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
long bonds in liquid Te, critical discuss for the analysis of EXAFS spectra is given using a cummulant expansion method which is known as a `model-independent' method [5]. 2. Experimental procedures To hold deeply supercooled state, small Te droplets with average diameter 20 nm were isolated in a NaCl matrix. As a result, the supercooled temperature range was more than 200°C below the melting point (450°C). EXAFS data at a Te K-absorption edge were taken in a transmission mode using a spectrometer at BL10B [6] station of the synchrotron radiation facility, Photon Factory (PF), in the National Laboratory for High Energy Physics (KEK), Tsukuba, Japan. Details in experimental procedure were written in a previous paper [2]. 3. EXAFS data
Fig. 1. EXAFS functions of supercooled liquid Te.
EXAFS functions, v(k), for supercooled liquid Te are shown in Fig. 1, where k means the wave number of a photoelectron. In general, EXAFS oscillation of liquid in high k region is damped at high temperature owing to disordered atomic arrangement and hence the contribution of neighbouring atoms weakly bonded to a central atom often fails to be resolved. However, we can get suf®cient information on the strongly bonded atoms. As seen in Fig. 1, EXAFS oscillations for liquid Te ÿ1 , which demonstrates that liqremain up to 12 A uid Te has covalently bonded chain structure. 4. Analysis Within a single scattering approximation [7], EXAFS around the K-absorption edge of m type element, vm k, is written as follows, 1 X Bn k Z 2r X Gmn r exp ÿ vm k k kn k n 0
sin 2kr /mn k dr r2
GXmn r 4pr2 gmn r;
where gmn r is the partial pair distribution function of n type element around a central m type element, and Bn k, /mn k and kn k are the backward scattering amplitude, the phase shift, and the mean free path of the photoelectron, respectively. The k-dependence of Bn k and /mn k is essential for distinguishing the species which surround the X-ray absorbing atom, but does not frequently give an accurate distribution function from EXAFS spectra. The APCFT (amplitudeand phase- corrected Fourier transform) method [8] is valid for removal of modulation by Bn k and /mn k and estimate the asymmetry of the distribution for a monatomic liquid. In the case of liquid Te, the APCFT is de®ned as FTe r
APCFT
kZ max
W k kmin
1a
1b
kvTe k BTe k
exp i 2kr /TeTe kdk;
2
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
where W(k) is the Hanning window function [7] to minimize the truncation eects of the Fourier transform, and BTe kand /TeTe k were determined from the experimental data of trigonal Te. The mean free path, kTe k, is calculated by the FEFF code [9]. In our APCFT procedure, the integrand of Eq. (2) was reduced by exp ÿ2R=kTe k according to the proposal by Stern et al. [10], where R is the bond length of Te±Te covalent bond in trigonal Te. Although the ®rst coordination shell in the liquid is broad compared with that of crystalline material, kTe k is larger compared with the dierence in the bond lengths between liquid Te and trigonal Te. Therefore, k-dependence of kTe k does not make a major contribution to the calculation of the APCFT. Fig. 2 shows the APCFT of liquid Te which includes the supercooled state. In the case that the distribution is harmonic-type, the peak of the imaginary part (denoted by dashed lines in the ®gure) is coincident with that (denoted by full lines) of the APCFT curve [9]. The break of this coincidence gives evidence that the distribution has an asymmetric form. One can see a coincidence for the supercooled liquid Te at the lowest tempera-
Fig. 2. APCFT of supercooled liquid Te. The magnitude; full line, the imaginary part; dashed line.
449
ture and a break of the coincidence with increasing temperature. Taking into account such asymmetry eects we adopted the cummulant expansion method [11,12]. A reduced EXAFS function including only ®rst coordination shell was obtained by a back Fourier transformation of APCFT. Then it was ®tted to a theoretical curve, T(k), containing cummulant coecients up to the 4th order, de®ned as 2 2 4 T k exp C0 ÿ 2k C2 C4 k 3 4 3 3 sin 2kC1 ÿ C3 k : 3 Here Cn is the cummulant coecient of nth order and the coordination number, N, the mean bond length, R, and the mean square displacement, d2 , are represented by exp(C0 ), C1 and C2 , respectively. It should be noticed that such a `modelindependent' method does not need any prior knowledge on the form of the distribution function. This has the obvious advantage that, after the EXAFS analysis has been completed, we can proceed to the discussion of structural models on a basis common to both supercooled liquid Te and liquid alkali±Te mixtures. Considering obvious truncation eects in Fourier transform, the same procedure as the Fourier ®ltering for the experimental spectrum was performed for the theoretical curve. As seen in Fig. 3, the ®tting curve (full line) is in a good agreement with the
Fig. 3. The reduced EXAFS function (open circles) of supercooled liquid Te at 250°C and the ®tting curve (full line).
450
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
experimental curve (open circles) for the supercooled liquid Te at 250°C. The ®tting range was ÿ1 . This smaller k limit, kmin , is rela5 6 k 6 12 A tively large compared with usual EXAFS analysis and mainly depends on a life time of the core hole in the X-ray absorbing atom [7]. The radial distribution functions were obtained by the splice method [10] and they are shown in Fig. 4. In this method, the cummulants obtained in the previous curve ®tting were used to construct kv(k) for 0 6 k 6 ks and it was then joined to the ÿ1 . experimental kv(k) at the splice point ks 5 A The resultant kv(k) was Fourier-transformed in ÿ1 . As seen in Fig. 4, there the k region up to 12 A appears a tail on the larger r side of the distribution function in the supercooled liquid state just below the melting point. With decreasing temperature, the peak increases and the tail on the larger r side becomes smaller. This asymmetry of the distribution function for liquid Te at a temperature close to the melting point can be easily understood, once the idea is accepted that long covalent bonds in addition to the usual short covalent bonds exist in liquid
Fig. 4. The radial distribution functions of supercooled liquid Te.
metallic Te. The distribution functions of supercooled liquid Te were ®tted with the sum of two Gaussian functions for convenience. Fig. 5 shows: (a) the coordination numbers and (b) the bond lengths of short and long bonds as a function of temperature. The fraction of the long bond decreases with decreasing temperature.
Fig. 5. (a) The coordination numbers of short (s) and long bonds (n) and the total coordination number (h). (b) The bond lengths of short (s) and long bonds (n).
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
Fig. 6 shows the Te±Te partial radial distribution functions of liquid alkali±Te mixtures. In principle, EXAFS at the Te K-edge for the alkali± Te mixtures should contain both Te±Te correlation term and Te±alkali correlation term. However, the Te±Te correlation is considered to be much stronger than that of the Te±alkali. This dierence is not only because the alkali concentration is a small fraction of the Te concentration but also because the bonding between Te and alkali atom is expected to be weaker than the Te±Te covalent bond. Moreover the alkali contribution in the ®tting k range is smaller owing to the relatively larger kmin . Therefore it is reasonable for us to assume that the Te±Te correlation mainly contributes to v(k) at the Te K-edge. The asymmetry in the Te±Te distribution function decreases by adding alkali to liquid Te even at a high temperature as shown in Fig. 6. The results of two Gaussian functions ®tting procedure are shown in the ®gure by the dashed line. The fraction of the long Te±Te bonds
Fig. 6. The radial distribution functions of liquid alkali±Te mixtures. The results of two Gaussian ®tting procedure are shown by the dashed lines. (a) liquid Te 410°C; (b) liquid K10 Te90 440°C; (c) liquid Rb10 Te90 440°C; (d) liquid Cs10 Te90 440°C.
451
tends to decrease upon the addition of alkali elements to pure liquid Te. Our EXAFS analysis, the model-independent method including the cummulant expansion procedure, convinces us that the structure of liquid alkali±Te mixtures is similar to that of supercooled liquid Te. 5. Discussion Both M±S transitions for supercooled liquid Te and alkali±Te mixtures are expected to give rise to the modulation of electronic structure for liquid metallic Te in a similar way. In the typical semiconducting chain such as liquid Se and crystalline Se and Te, two of the four p-electrons form the r bondings between neighbouring atoms and the retained two electrons occupy lone pair (LP) orbital. In liquid metallic Te, a frequent charge transfer from LP orbitals to antibonding orbitals in the neighbouring chains occurs by thermal agitation. There appear chain molecules composed of only few atoms scissored at high temperature. The chain ends carry negative charge, and the midchain atoms have a corresponding positive charge associated with hole since an electron tends to be transferred into the p-orbital of the broken bonds. The inter- and intra-charge-transfers result in ¯uctuations of charge distribution in the chain molecule: creation of the long bonds and holes in the LP orbitals. The average chain length of liquid Te is estimated to be about 10 atoms by Misawa [13] and 3 atoms by Silva and Cutler [14] just above the melting point. Thus, a positively charged midchain atom attracts the chain end of neighbouring molecules, which strengthens interchain coupling and induces further charge transfer among neighbouring Te chains. As a result, volume contracts and hole conduction is induced. The M±S transition upon the addition of alkalis to liquid Te is explained in these terms. The electron transferred from alkali to Te ®lls the hole in LP orbital, which not only decreases carrier density but also induces structural modi®cation by the repulsion between LP orbitals. Shimojo et al. [15] have calculated the atomic and elec-
452
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
tronic structure of liquid Rb±Te mixtures by means of ab initio molecular-dynamics and shown that the interaction between two Te chains are suppressed by the presence of alkali elements, and as a result the twofold-coordinated chain becomes more stable. Complete charge transfer from alkalis to Te chains hinders the charge ¯uctuations in Te chains.
Acknowledgements We would like to thank Professors K. Hoshino and A. Ikawa and Dr F. Shimojo for helpful discussions. This work was supported by a Grant-inAid from The Ministry of Education, Science, Sports and Culture. References
6. Summary EXAFS spectra of supercooled liquid Te and liquid alkali±Te mixtures were carefully analysed by adopting a `model-independent' method. It is found that the shortened chains in liquid Te with metallic nature are composed of short(2.80 A) covalent bonds and that the and long(2.95 A) long bonds vanish on the M±S transition. We suggests that in the liquid Te near the melting point charge transfer from lone pair (LP) orbitals to anti-bonding orbitals results in charge ¯uctuations in the chain molecule; creation of 3-electron bond (the long bond) and appearance of a hole into the LP orbitals. In the case of liquid alkali±Te mixtures, charge transfer from alkali to Te reduces, rather than add to, the charge ¯uctuations in Te chains. Similar mechanism is also expected in the case of the semiconductor-metal transition observed for liquid Se at a high temperature.
[1] T. Tsuzuki, M. Yao, H. Endo, J. Phys.: Soc. Jpn. 64 (1995) 485. [2] Y. Kawakita, M. Yao, H. Endo, J. Phys. Soc. Jpn. 66 (1997) 1339. [3] Y. Tsuchiya, J. Phys.: Condens. Matter 3 (1991) 3163. [4] J. Fortner, M.-L. Saboungi, J.E. Enderby, Phys. Rev. Lett. 69 (1992) 1415. [5] E.D. Crozier, J.J. Rehr, R. Ingalls, in: D.C. Koningsberger, R. Prins (Eds.), X-Ray Absorption, Wiley, New York, 1988, p. 403. [6] M. Nomura, A. Koyama, Photon Factory Activity Report 7 (1989) 87. [7] B.K. Teo, EXAFS: Basic Principles and Data Analysis, Springer, Berlin, 1986. [8] P.A. Lee, G. Beni, Phys. Rev. B 15 (1977) 2862. [9] J.J. Rehr, J. Mustre de Leon, S.I. Zabinsky, R.C. Albers, J. Am. Chem. Soc. 113 (1991) 5135. [10] R. Kubo, J. Phys. Soc. Jpn. 17 (1962) 1100. [11] G. Bunker, Nucl. Instrum. Meth. 207 (1983) 437. [12] E.A. Stern, Y. Ma, O. Hanske-Petitpierre, C.E. Bouldin, Phys. Rev. B 46 (1992) 687. [13] M. Misawa, J. Phys.: Condens. Matter 4 (1992) 9491. [14] L.A. Silva, M. Cutler, Phys. Rev. B 42 (1990) 7103. [15] F. Shimojo, K. Hoshino, Y. Zempo, these Proceedings, p. 547.
www.elsevier.com/locate/jnoncrysol
Short and long bonds in liquid tellurium Y. Kawakita a
a,* ,
M. Yao b, H. Endo
c
Faculty of Science, Department of Physics, Kyushu University, 4-2-1 Ropponmatsu, Fukuoka 810-8560, Japan b Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan c Faculty of Engineering, Fukui Institute of Technology, 3-6-1 Gakuen, Fukui 910-8505, Japan
Abstract Liquid tellurium (Te) is metallic, which is caused by the strong interaction between neighbouring chain-molecules. With decreasing temperature from the melting point (450°C) to a supercooled state (250°C), liquid Te undergoes a transition from a metal to a semiconductor (M±S transition) being accompanied by volume expansion. Our EXAFS data for supercooled liquid Te were carefully analyzed by adopting a `model-independent' method. It is found that the and long(2.95 A) covalent bonds and short chains in liquid Te with metallic nature are composed of short(2.80 A) that the long bonds vanish on the M±S transition. The M±S transition described above also occurs by the addition of an alkali to liquid Te. The relation of the existence of long covalent bond and the metallic behavior is explained in term of charge ¯uctuations in the chain molecule. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Various measurements such as EXAFS, neutron scattering and conductivity have been carried out on liquid Te by our group [1,2]. Important ®ndings are that liquid metallic Te near the melting point has a covalently bonded chain structure composed of short and long bonds [1]. The existence of two-type bonds leads to the key question: What is the mechanism that links the metallic properties with the bonding con®guration? Recent results for the deeply supercooled liquid Te and the liquid alkali±Te mixtures provide essential information [1,2]. When liquid Te is supercooled to 250°C, it undergoes a transition from a metal to a semiconductor (M±S transition) being accompanied by a volume expansion [3]. We sug-
* Corresponding author. Tel.: +81 92 726 4734; fax: +81 92 726 4728; e-mail: [email protected]
gested based on analysis of EXAFS data that the fraction of long bonds decreases on approaching to the M±S transition region [1]. The M±S transition is also observed when alkalis such as Na, K, Rb and Cs are added to liquid Te. These eects are accompanied by a decrease of interchain correlation [2,4] and a decrease of the long bond fraction [2]. The large electronegativity dierence suggests the substantial charge transfer from the alkali atom to the Te. In fact, the compositional and temperature dependence of conductivity are almost independent of the alkali species [2]. This M±S transition observed for the liquid alkali±Te mixtures also leads to the assumption that the presence of long bonds is closely related to the metallic properties of liquid Te. The purpose of this paper is to establish a microscopic scenario for the M±S transition in terms of the fraction of long bonds on a basis common to both supercooled liquid Te and liquid alkali±Te mixtures. To recon®rm the presence of
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 2 7 5 - 6
448
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
long bonds in liquid Te, critical discuss for the analysis of EXAFS spectra is given using a cummulant expansion method which is known as a `model-independent' method [5]. 2. Experimental procedures To hold deeply supercooled state, small Te droplets with average diameter 20 nm were isolated in a NaCl matrix. As a result, the supercooled temperature range was more than 200°C below the melting point (450°C). EXAFS data at a Te K-absorption edge were taken in a transmission mode using a spectrometer at BL10B [6] station of the synchrotron radiation facility, Photon Factory (PF), in the National Laboratory for High Energy Physics (KEK), Tsukuba, Japan. Details in experimental procedure were written in a previous paper [2]. 3. EXAFS data
Fig. 1. EXAFS functions of supercooled liquid Te.
EXAFS functions, v(k), for supercooled liquid Te are shown in Fig. 1, where k means the wave number of a photoelectron. In general, EXAFS oscillation of liquid in high k region is damped at high temperature owing to disordered atomic arrangement and hence the contribution of neighbouring atoms weakly bonded to a central atom often fails to be resolved. However, we can get suf®cient information on the strongly bonded atoms. As seen in Fig. 1, EXAFS oscillations for liquid Te ÿ1 , which demonstrates that liqremain up to 12 A uid Te has covalently bonded chain structure. 4. Analysis Within a single scattering approximation [7], EXAFS around the K-absorption edge of m type element, vm k, is written as follows, 1 X Bn k Z 2r X Gmn r exp ÿ vm k k kn k n 0
sin 2kr /mn k dr r2
GXmn r 4pr2 gmn r;
where gmn r is the partial pair distribution function of n type element around a central m type element, and Bn k, /mn k and kn k are the backward scattering amplitude, the phase shift, and the mean free path of the photoelectron, respectively. The k-dependence of Bn k and /mn k is essential for distinguishing the species which surround the X-ray absorbing atom, but does not frequently give an accurate distribution function from EXAFS spectra. The APCFT (amplitudeand phase- corrected Fourier transform) method [8] is valid for removal of modulation by Bn k and /mn k and estimate the asymmetry of the distribution for a monatomic liquid. In the case of liquid Te, the APCFT is de®ned as FTe r
APCFT
kZ max
W k kmin
1a
1b
kvTe k BTe k
exp i 2kr /TeTe kdk;
2
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
where W(k) is the Hanning window function [7] to minimize the truncation eects of the Fourier transform, and BTe kand /TeTe k were determined from the experimental data of trigonal Te. The mean free path, kTe k, is calculated by the FEFF code [9]. In our APCFT procedure, the integrand of Eq. (2) was reduced by exp ÿ2R=kTe k according to the proposal by Stern et al. [10], where R is the bond length of Te±Te covalent bond in trigonal Te. Although the ®rst coordination shell in the liquid is broad compared with that of crystalline material, kTe k is larger compared with the dierence in the bond lengths between liquid Te and trigonal Te. Therefore, k-dependence of kTe k does not make a major contribution to the calculation of the APCFT. Fig. 2 shows the APCFT of liquid Te which includes the supercooled state. In the case that the distribution is harmonic-type, the peak of the imaginary part (denoted by dashed lines in the ®gure) is coincident with that (denoted by full lines) of the APCFT curve [9]. The break of this coincidence gives evidence that the distribution has an asymmetric form. One can see a coincidence for the supercooled liquid Te at the lowest tempera-
Fig. 2. APCFT of supercooled liquid Te. The magnitude; full line, the imaginary part; dashed line.
449
ture and a break of the coincidence with increasing temperature. Taking into account such asymmetry eects we adopted the cummulant expansion method [11,12]. A reduced EXAFS function including only ®rst coordination shell was obtained by a back Fourier transformation of APCFT. Then it was ®tted to a theoretical curve, T(k), containing cummulant coecients up to the 4th order, de®ned as 2 2 4 T k exp C0 ÿ 2k C2 C4 k 3 4 3 3 sin 2kC1 ÿ C3 k : 3 Here Cn is the cummulant coecient of nth order and the coordination number, N, the mean bond length, R, and the mean square displacement, d2 , are represented by exp(C0 ), C1 and C2 , respectively. It should be noticed that such a `modelindependent' method does not need any prior knowledge on the form of the distribution function. This has the obvious advantage that, after the EXAFS analysis has been completed, we can proceed to the discussion of structural models on a basis common to both supercooled liquid Te and liquid alkali±Te mixtures. Considering obvious truncation eects in Fourier transform, the same procedure as the Fourier ®ltering for the experimental spectrum was performed for the theoretical curve. As seen in Fig. 3, the ®tting curve (full line) is in a good agreement with the
Fig. 3. The reduced EXAFS function (open circles) of supercooled liquid Te at 250°C and the ®tting curve (full line).
450
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
experimental curve (open circles) for the supercooled liquid Te at 250°C. The ®tting range was ÿ1 . This smaller k limit, kmin , is rela5 6 k 6 12 A tively large compared with usual EXAFS analysis and mainly depends on a life time of the core hole in the X-ray absorbing atom [7]. The radial distribution functions were obtained by the splice method [10] and they are shown in Fig. 4. In this method, the cummulants obtained in the previous curve ®tting were used to construct kv(k) for 0 6 k 6 ks and it was then joined to the ÿ1 . experimental kv(k) at the splice point ks 5 A The resultant kv(k) was Fourier-transformed in ÿ1 . As seen in Fig. 4, there the k region up to 12 A appears a tail on the larger r side of the distribution function in the supercooled liquid state just below the melting point. With decreasing temperature, the peak increases and the tail on the larger r side becomes smaller. This asymmetry of the distribution function for liquid Te at a temperature close to the melting point can be easily understood, once the idea is accepted that long covalent bonds in addition to the usual short covalent bonds exist in liquid
Fig. 4. The radial distribution functions of supercooled liquid Te.
metallic Te. The distribution functions of supercooled liquid Te were ®tted with the sum of two Gaussian functions for convenience. Fig. 5 shows: (a) the coordination numbers and (b) the bond lengths of short and long bonds as a function of temperature. The fraction of the long bond decreases with decreasing temperature.
Fig. 5. (a) The coordination numbers of short (s) and long bonds (n) and the total coordination number (h). (b) The bond lengths of short (s) and long bonds (n).
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
Fig. 6 shows the Te±Te partial radial distribution functions of liquid alkali±Te mixtures. In principle, EXAFS at the Te K-edge for the alkali± Te mixtures should contain both Te±Te correlation term and Te±alkali correlation term. However, the Te±Te correlation is considered to be much stronger than that of the Te±alkali. This dierence is not only because the alkali concentration is a small fraction of the Te concentration but also because the bonding between Te and alkali atom is expected to be weaker than the Te±Te covalent bond. Moreover the alkali contribution in the ®tting k range is smaller owing to the relatively larger kmin . Therefore it is reasonable for us to assume that the Te±Te correlation mainly contributes to v(k) at the Te K-edge. The asymmetry in the Te±Te distribution function decreases by adding alkali to liquid Te even at a high temperature as shown in Fig. 6. The results of two Gaussian functions ®tting procedure are shown in the ®gure by the dashed line. The fraction of the long Te±Te bonds
Fig. 6. The radial distribution functions of liquid alkali±Te mixtures. The results of two Gaussian ®tting procedure are shown by the dashed lines. (a) liquid Te 410°C; (b) liquid K10 Te90 440°C; (c) liquid Rb10 Te90 440°C; (d) liquid Cs10 Te90 440°C.
451
tends to decrease upon the addition of alkali elements to pure liquid Te. Our EXAFS analysis, the model-independent method including the cummulant expansion procedure, convinces us that the structure of liquid alkali±Te mixtures is similar to that of supercooled liquid Te. 5. Discussion Both M±S transitions for supercooled liquid Te and alkali±Te mixtures are expected to give rise to the modulation of electronic structure for liquid metallic Te in a similar way. In the typical semiconducting chain such as liquid Se and crystalline Se and Te, two of the four p-electrons form the r bondings between neighbouring atoms and the retained two electrons occupy lone pair (LP) orbital. In liquid metallic Te, a frequent charge transfer from LP orbitals to antibonding orbitals in the neighbouring chains occurs by thermal agitation. There appear chain molecules composed of only few atoms scissored at high temperature. The chain ends carry negative charge, and the midchain atoms have a corresponding positive charge associated with hole since an electron tends to be transferred into the p-orbital of the broken bonds. The inter- and intra-charge-transfers result in ¯uctuations of charge distribution in the chain molecule: creation of the long bonds and holes in the LP orbitals. The average chain length of liquid Te is estimated to be about 10 atoms by Misawa [13] and 3 atoms by Silva and Cutler [14] just above the melting point. Thus, a positively charged midchain atom attracts the chain end of neighbouring molecules, which strengthens interchain coupling and induces further charge transfer among neighbouring Te chains. As a result, volume contracts and hole conduction is induced. The M±S transition upon the addition of alkalis to liquid Te is explained in these terms. The electron transferred from alkali to Te ®lls the hole in LP orbital, which not only decreases carrier density but also induces structural modi®cation by the repulsion between LP orbitals. Shimojo et al. [15] have calculated the atomic and elec-
452
Y. Kawakita et al. / Journal of Non-Crystalline Solids 250±252 (1999) 447±452
tronic structure of liquid Rb±Te mixtures by means of ab initio molecular-dynamics and shown that the interaction between two Te chains are suppressed by the presence of alkali elements, and as a result the twofold-coordinated chain becomes more stable. Complete charge transfer from alkalis to Te chains hinders the charge ¯uctuations in Te chains.
Acknowledgements We would like to thank Professors K. Hoshino and A. Ikawa and Dr F. Shimojo for helpful discussions. This work was supported by a Grant-inAid from The Ministry of Education, Science, Sports and Culture. References
6. Summary EXAFS spectra of supercooled liquid Te and liquid alkali±Te mixtures were carefully analysed by adopting a `model-independent' method. It is found that the shortened chains in liquid Te with metallic nature are composed of short(2.80 A) covalent bonds and that the and long(2.95 A) long bonds vanish on the M±S transition. We suggests that in the liquid Te near the melting point charge transfer from lone pair (LP) orbitals to anti-bonding orbitals results in charge ¯uctuations in the chain molecule; creation of 3-electron bond (the long bond) and appearance of a hole into the LP orbitals. In the case of liquid alkali±Te mixtures, charge transfer from alkali to Te reduces, rather than add to, the charge ¯uctuations in Te chains. Similar mechanism is also expected in the case of the semiconductor-metal transition observed for liquid Se at a high temperature.
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